If we do not based on Higgs mechanism and give a Constraint to the ga. nge invariant Lagrangian of SU(2)×U(1)unified theory of weak and el. ectromagnetic interaction of the leptons.Then the variation of the action Convert to the variational problems with subsidiary Conditons.We Cons. ider the transformations properties under the gange transformations of this Constrained System.Which lead to the results that effective Lagran. gian Coataining Lagrangian multiplier may has the mass terms of interm. ediate bosons.Except the Lagrangian multiplier terms.The effective Lag. rangian agree with the W-S theory.The resulting theory perhaps might be renormalizable due to the Lagrangian multipler terms.